WASHINGTON (Reuters) - The Federal Reserve faces a “quite challenging” period in trying to keep the U.S. recovery on track amid a risk that low unemployment could lead to an overheated economy, former Fed chief Janet Yellen said on Friday.

“The question for the Fed is how to manage monetary policy to try to keep the expansion going for a long time. And it is going to be quite challenging,” Yellen said at an event in Washington, referring to the central bank’s dilemma of keeping inflation from spiking without curbing economic growth.

With the economy effectively at full employment or even beyond it, wages and prices in theory should rise as businesses bid for employees and workers have more to spend. Though it has not become apparent in the data yet, Yellen said she would still be concerned.

“At a time like this I would be worried that the economy is in a situation where it could overheat. I don’t think it would be very rapid. But I think it could occur,” she said in remarks to reporters at the Brookings Institution.

Yellen has kept a low public profile in the seven months since turning over the reins of the Fed to Jerome Powell.

In a paper presented at the Brookings Institution earlier on Friday, Yellen suggested the Fed, ahead of the next recession, should make an explicit commitment to keep interest rates low until the impact of the next downturn is fully offset - a significant change from how monetary policy is currently conducted.

The Fed has raised rates twice this year and is expected to do so again at its Sept. 25-26 policy meeting.

Yellen also delved into the current challenge facing Fed chief Powell and his colleagues. Boston Fed President Eric Rosengren, in a paper released this week, noted that the Fed’s track record of managing levels of ultra-low unemployment was not good. They are typically followed by recessions.

The current unemployment rate of 3.9 percent is at a level where the Fed needs to watch its next steps carefully, Yellen suggested.

Current projections show the Fed continuing to tighten policy “to relieve a little bit of pressure on the labor market over time,” Yellen said. “It has almost never happened that the unemployment rate has risen without a recession ... Is it going to be possible to pull this off successfully without being the cause of the next recession?”